The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered
a huge amount of innovative scientific inquiry. In the almost three decades since, much has …

The structures, the phase diagrams, and the appearance of a neutron resonance signaling
an unconventional superconducting state provide phenomenological evidence relating the …

We examine the interplay of symmetry and topological order in 2+ 1-dimensional topological
quantum phases of matter. We present a precise definition of the topological symmetry …

This article reviews the physics of high-temperature superconductors from the point of view
of the doping of a Mott insulator. The basic electronic structure of cuprates is reviewed …

Recently developed numerical methods have enabled the explicit construction of the
superconducting state of the Hubbard model of strongly correlated electrons in parameter …

The enormous experimental progress in atomic, molecular, and optical (AMO) physics
during the last decades allows us nowadays to isolate single, a few or even many-body …

Quantum magnets have occupied the fertile ground between many-body theory and low-
temperature experiments on real materials since the early days of quantum mechanics …

We classify distinct types of quantum number fractionalization occurring in two-dimensional
topologically ordered phases, focusing in particular on phases with Z 2 topological order …

A theoretical review is given on high temperature superconductivity in copper oxides
(cuprates) by focusing on the hole doping cases based on the view that it is realized in …

This review gives a rather general discussion of high temperature superconductors as an
example of a strongly correlated material. The argument is made that in view of the many …